A convex body in RP^n is an ellipsoid if its hypersections through two fixed interior points are paired by harmonic homologies for every (n-2)-plane in a given hyperplane.
A note on the false center problem,Mathematika21(1974), 216−27
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A characterization of the ellipsoid in terms of pairs of sections associated by a harmonic homology
A convex body in RP^n is an ellipsoid if its hypersections through two fixed interior points are paired by harmonic homologies for every (n-2)-plane in a given hyperplane.